Is it permissible to play with a dog, or feed it, or give it water, especially if it has been neglected by its Christian owner? And do the angels not enter an apartment that has a dog in it, or the entire building?

Feeding and watering a dog are acts of kindness commanded by Islamic law. It is permissible to play with a dog as long as it does not require touching it. If it requires touching, then it is not permissible. The presence of a dog in one of the apartments of a building does not prevent angels from entering the rest of the apartments.